Simplify the following expression: $r = \dfrac{-5t^2 + 5t + 10}{t - 2} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ r =\dfrac{-5(t^2 - 1t - 2)}{t - 2} $ Then we factor the remaining polynomial: $t^2 {-1}t {-2} $ ${-2} + {1} = {-1}$ ${-2} \times {1} = {-2}$ $ (t {-2}) (t + {1}) $ This gives us a factored expression: $\dfrac{-5(t {-2}) (t + {1})}{t - 2}$ We can divide the numerator and denominator by $(t + 2)$ on condition that $t \neq 2$ Therefore $r = -5(t + 1); t \neq 2$